 Hi and welcome to our session. Let us discuss the following question. The question says in figure 10.37, angle PQR is equal to 100 degree where PQ and R are points on a circle with center O. Find angle OPR. Let's now pick in the solution. We are given that angle PQR is equal to 100 degree and we have to find angle OPR. Now since major RPR, this is the major RPR, subtends reflex angle POR, this one, at the center PQR at point Q on remaining part of the circle. Therefore, reflex angle POR is equal to 2 times angle PQR by theorem 10.8 given in your MCERRT book and with state star, the angle subtended by an arc at the center is double, will subtended by it at any point on the remaining part of the circle. We know that angle PQR is equal to 100 degree, so reflex angle POR is equal to 200 degree. Now we know that angle POR plus reflex angle POR is equal to 360 degree, so this means angle POR is equal to 360 degree minus reflex angle POR and this is equal to 360 degree minus 200 and this comes out to be 160 degree, so angle POR is equal to 160 degree, this angle is of 160 degree. Now we will consider triangle OPR, in triangle OPR, P is equal to OR because these are radius of the same circle. Now as OP is equal to OR, therefore angle OPR is equal to angle ORP because angles opposite to equal sides are equal, so now let angle OPR and angle ORP be equal to x degree. Now angle OPR plus angle ORP plus angle POR is equal to 180 degree because sum of all angles of a triangle is 180 degree. Now substitute the value of angle OPR, angle ORP and angle POR in this equation, angle OPR is equal to x degree, angle ORP is equal to x degree, angle POR is equal to 160 degree, this implies 2x degree plus 160 degree is equal to 180 degree, this implies 2x degree is equal to 20 degree and this implies x degree is equal to 10 degree, so angle OPR is equal to 10 degree, this is our required answer, so this completes the session, bye and take care.